Express the following complex numbers in r cos i sin form

Express the following complex numbers in r (cos + i sin ) form.

a. 5+5i

b. 3 square root3+3i

c. 0+4i
d. 2

a. 5 + 5 i

r=sqrt(x^2 + y^2) = sqrt(25+25)=5sqrt2

theta=tan^-1(y/x) = tan^-11=pi/4

(5 sqrt2 cos (pi/4)+ 5i sqrt 2 sin(pi/4))

b. -3 sqrt 3 + 3i

r=sqrt(27+9)=6

theta=tan^-1(-3/3sqrt3)= 5pi/6

(6 cos (5pi/6)+ i sin (5pi/6))

c. 0 + 4i

r=4

theta=tan^-1(4/0)=pi/2

4cospi/2 + 4 sin pi/2